The primary advantage of using the complex forcing function method to solve for the sinusoidal steady-state response is that it transforms the circuit's governing equation from what to what?
Explanation
This question gets to the core reason for using phasor and complex impedance methods: the transformation of difficult-to-solve differential equations into simple algebraic ones.
Other questions
In the context of sinusoidal steady-state analysis, what is the term for the abbreviated complex representation of a real sinusoidal current or voltage, which contains only amplitude and phase information?
What is the correct phasor representation V for the time-domain voltage v(t) = 100 cos(400t - 30 degrees) volts?
For a sinusoidal steady-state circuit, what is the relationship between the phasor voltage V across an inductor and the phasor current I through it?
What is the correct phasor relationship between the current I and voltage V for a capacitor in a sinusoidal steady-state circuit?
A sinusoidal voltage source vs(t) = 40 cos(8000t) V is applied to a series RL circuit. The resulting steady-state current is measured. According to Practice problem 10.3, what is the value of the inductor voltage, vL, at t = 0?
What are the three mandatory conditions that must be met to compare the phase relationship between two sinusoidal waves?
Find the angle by which the current i1 = 1.4 sin(120 pi t - 70 degrees) A lags the voltage v1 = 120 cos(120 pi t - 40 degrees) V.
In the frequency domain, what is the definition of impedance (Z)?
What is the correct relationship between admittance (Y), conductance (G), and susceptance (B)?
A 5 mH inductor is in series with a 100 microFarad capacitor. What is the equivalent impedance of this combination at a frequency of omega = 10,000 rad/s?
What is the equivalent impedance of the parallel combination of a 5 mH inductor and a 100 microFarad capacitor at an operating frequency of omega = 10,000 rad/s?
A circuit consists of a 1000 ohm resistor in series with a 1 mF capacitor. What is the equivalent impedance of the circuit at an operating frequency of 20 rad/s?
In a frequency-domain circuit with two nodes V1 and V2, the KCL equation at node V1 is (0.2 + j0.2)V1 - j0.1V2 = 1. The KCL equation at node V2 is -j0.1V1 + (0.1 - j0.1)V2 = j0.5. What is the phasor voltage V1?
A frequency-domain circuit is analyzed using mesh analysis, yielding the equations: (3 + j4)I1 - j4I2 = 10 and (2 - j4)I1 + j2I2 = 0. What is the value of the phasor mesh current I2?
When analyzing a linear circuit with multiple sinusoidal sources operating at different frequencies, what analysis technique must be used?
Find the Thévenin equivalent impedance Zth seen by the -j10 ohm impedance in the circuit described in Example 10.11.
In a phasor diagram for a series RLC circuit, if the current phasor I is used as the reference (along the positive real axis), how would the voltage phasor for the inductor, VL, be oriented?
What is the inductive reactance of a 30 mH inductor at a frequency of 1000 rad/s?
What is the impedance of a 2 pF capacitor at an operating frequency of ω = 3000 rad/s?
Transform the time-domain current i(t) = -5 sin(580t - 110 degrees) A into its standard cosine-based phasor form.
Given the phasor current I = 20 + j10 A, and an operating frequency of omega = 2000 rad/s, what is the instantaneous value of the current at t = 1 ms?
A sinusoidal voltage of 8 / -50 degrees V at a frequency of 100 rad/s is applied to a 4 H inductor. What is the resulting phasor current?
For a simple RC circuit with a complex source of 3e^(j5t) V, a 1 ohm resistor, and a 2 F capacitor, the resulting steady-state capacitor voltage is found to be 29.85 cos(5t - 84.3 degrees) mV. What was the complex phasor Vm for the capacitor voltage?
In the frequency-domain circuit of Figure 10.21, with a source of 100/0 degrees V, a resistor -j5 ohms, a resistor 5 ohms, and an inductor j5 ohms, what is the phasor current I1?
What is the equivalent impedance Zeq for the circuit in Example 10.7, which has a 1.5 kOhm resistor in series with the parallel combination of a 1 kOhm resistor and an inductor with impedance j1 kOhm, and a capacitor with impedance -j2 kOhm?
A circuit has a source vs(t) = 40 sin(3000t) V. What is the correct phasor representation Vs to use for frequency-domain analysis?
In a linear circuit, a sinusoidal forcing function Vm cos(ωt + θ) produces a steady-state response Im cos(ωt + φ). If the forcing function is changed to jVm sin(ωt + θ), what is the resulting response?
The steady-state response of a circuit is found by assuming a solution composed of the forcing function plus what other functions?
A series RL circuit with R=20 ohms and L=30 mH is driven by a voltage source vs = 8 cos(1000t) V. What is the steady-state current iL(t)?
How does Kirchhoff's Voltage Law (KVL) apply to phasors in the frequency domain?
In the RLC circuit of Example 10.5, two sources operate at omega = 2 rad/s. The capacitor current is Ic = 2 / 28 degrees A. What is the voltage Vc across the capacitor, which has an impedance of -j/2 ohms?
What is the key difference between analyzing a resistive circuit with a sinusoidal source versus analyzing an RL or RC circuit with a sinusoidal source using time-domain differential equations?
The term 'steady-state response' in the context of sinusoidal sources refers to what condition?
A circuit contains two sinusoidal sources: one at 3 cos(5t) A and another at 2 cos(3t) A. To find the power dissipated by a 10 ohm resistor in the circuit, what is the correct procedure?
The resistive component of an impedance Z = R + jX is 8 ohms, but it is part of a parallel RL circuit. Is the resistance of the physical resistor in the circuit necessarily 8 ohms?
A complex current 4e^(j800t) A is applied to the series combination of a 1 mF capacitor and a 2 ohm resistor. What is the resulting complex voltage?
What is the equivalent admittance Yeq for a circuit with impedance Zeq = 2 + j1.5 kOhms?
In a parallel RC circuit with a single voltage V across both components, what is the relationship between the capacitor current phasor Ic and the resistor current phasor Ir in a phasor diagram?
If a time domain voltage is v(t) = 115 sin(500t + 45 degrees) volts, what is the correct representation using a cosine function?
A sinusoidal forcing function is described by Vm cos(ωt). The forced response in a series RL circuit is found to be I(t) = A cos(ωt - θ). What is the expression for the amplitude A?
For the frequency-domain circuit in Practice 10.12, what is the node voltage V1?
In the analysis of the high-frequency hybrid-pi transistor model in Section 10.7, why does the amplifier gain decrease as frequency increases?
A complex number is given as (2-j7)/(3-j). What is its representation in polar form?
An RLC circuit has a source that provides a voltage of 10 cos(1000t) V. The circuit has a 3 ohm resistor, a 4 mH inductor, and a capacitor. The circuit also contains a dependent source of 2*I1. The mesh equations are (3+j4)I1 - j4I2 = 10 and (2-j4)I1 + j2I2 = 0. What is the time-domain expression for the current i1(t)?
In a phasor diagram, if the voltage phasor V is 1/0 degrees and the current phasor I is 0.2 + j0.1 A, what is the geometric relationship between them?
What is the primary reason for using a double-headed arrow to indicate mutual coupling between two coils in a circuit diagram?
If two sinusoidal voltages are v1 = 120 cos(120 pi t - 40 degrees) V and v2 = -0.8 cos(120 pi t - 110 degrees) A, what is the angle by which i1 (v2) lags v1?
For an RLC circuit with a source vs(t) operating at 40 sin(3000t) V, a 1.5 kOhm resistor, an inductor with impedance j1 kOhm and a capacitor with impedance -j2 kOhm, what is the phasor current I?
A general sinusoidal current i(t) = Im cos(ωt + φ) is transformed into a phasor I by a series of steps. Which of the following correctly describes the final step of the transformation?